Assuming the relationship in question is the one between Jem and Scout, we can see changes to their relationship in the arrangement between Jem and Scout in going to the Halloween festival.

In the past, the two would probably have gone together to the festival. However, at this stage in Jem's development, he is "man enough" to escort Scout. He does not go with her, but takes her there as an escort, protector, etc., not as a playmate.

If you have to choose a relationship, one that I find interesting is Alexandra's and Atticus's relationship. They seem to have a non-existent one until she comes to live with them, and then it turns rocky as Atticus feels she is interfering. However we learn that she does care about him and have sympathy for him.

The final scene where Scout and Jem are walking home from the school for the pageant is a great example of how their relationship has developed. At the beginning of the story, Jem wants very little to do with his kid sister, and is more interested in Dill and Boo Radley than he is in playing with her or including her.

But in this final scene, the two are walking and talking and Jem has lost his sense of annoyance in his sister. In fact, he takes on a very protective role when he hears something behind them. He does make fun of Scout when she believes the noise to be Cecil Jacobs (as he might have in the beginning of the book), and then, when they are attacked, Jem puts himself between the attacker and his sister.

A relationship seems to have become stronger between Atticus Finch and Mr. Underwood. First they are merely the occupants of the building where there offices are located. But, on the night that Atticus sits beneath a bare bulb, propped in his car against the jailhouse door, purportedly reading the paper as the mob appears in order to take Tom Robinson from the jail, Mr. Underwood, who obviously has been watching the proceedings, points his shotgun at the men from his office window and "covers" Atticus.

Further, as he is known for disliking Negroes, Mr. Underwood shocks the Maycomb community with his editorial about the cruel treatment and demise of Tom Robinson in the Maycomb Tribune. Obviously, from the example of Atticus Finch, Mr. Underwood has learned to examine some of his own notions, and he has come away with a new respect for Atticus.

Scout and Aunt Alexandra have managed to bury the hatchet, and their relationship is much better than before. Alexandra appreciates Scout's ladylike ways at the Missionary Circle tea, and after Scout returns home after Bob Ewell's assault on the children, Alexandra blames herself for the attack and repeatedly calls her "darling." In an act of compromise and acceptance, Alexandra brings Scout "my overalls... the garments she most despised."